Many fluid products are packaged in a collapsible bladder, with a suitable closing and dispensing system, after the bladder has been inserted into a rigid, molded plastic container through the finish of the container. A container of this type must be able to vent the portion of its interior that is exterior to the bladder to accommodate expansion of the bladder during its filling with the fluid product, and then to accommodate collapse of the bladder as the fluid product is dispensed therefrom. Heretofore, these venting requirements have been met by drilling a hole in the bottom of the container at a location away from the exterior of the bladder in a separate, post-molding operation. This post-molding operation adds to the cost of manufacture of containers of this type in a production operation, and it can restrict the productive capacity of a container blowing machine.